NEW YORK (NYTIMES) - Mrs Hillary Clinton and Mr Donald Trump kept fact-checkers busy throughout their first debate as they sparred over their policies and records on the economy, national security, the environment and their own personal pasts.

Foreign Policy and National Security: The Fight Against Isis

Mr Trump said Mrs Clinton had been "fighting ISIS your entire adult life".

In reality, the Islamic State, also known as ISIS or ISIL, began as an Al-Qaeda affiliate that sprang up in Iraq as the Sunni insurgency amid the power vacuum created by the 2003 US invasion that toppled Saddam Hussein's government.

It was largely defeated and pushed into Syria during the Obama administration's first term, when Mrs Clinton was secretary of state. It eventually split from the original Al-Qaeda and rebranded itself as ISIS, sweeping back into Iraq in 2014, when she was out of office.

Cyberattacks

Mrs Clinton blamed Russia for conducting cyberattacks, saying Russia and President Vladimir Putin of Russia were playing a "long game" here.

She's right, but the United States has not yet publicly named Russia as the attacker against the Democratic National Committee, much less the State Department, the White House and the Joint Chiefs.

"The United States has much greater capacity," she said, seeming to threaten that the United States could respond in kind. She appeared to be referring to Washington's offensive cyberability, made clear in the US attacks on Iran's nuclear programme, code-named "Olympic Games", which played out while she was secretary of state. Again, the United States has never admitted to that cyberoffensive action.

Mr Trump seemed to try to deflect responsibility away from Moscow. "It could be Russia," he said, "but it could also be China." US intelligence officials disagree: This most recent round of attacks, they concluded with "high confidence", indeed originated from Russia.

ISIS and Iraqi Oil

Mr Trump said the ISIS would never have come into power if the United States had stayed in Iraq, and if the United States had "taken the oil", especially in Libya.

The assertion is impossible to disprove, but it's unlikely that 10,000 troops remaining in Iraq would have made much of a difference - especially in Syria and Libya, where the United States never had troops. Moreover, much of the Islamic State's revenue has come from smuggling and taxes on local people, and much of the oil infrastructure has been destroyed, as has the Islamic State's transportation network.

Mr Trump said the United States should have taken Iraq's oil.

It is an assertion he made a few weeks ago, and one that was roundly criticised at the time. Seizing Iraq's oil - or the resources of any country - is illegal under international law, and doing so would have likely prompted condemnation from around the world. In purely practical terms, seizing Iraq's oil would have required tens of thousands of US troops to protect Iraq's oil infrastructure, which is spread out across the country and largely above ground. It also is probably safe to assume that Iraqis themselves would have objected to their country's main source of wealth being used to enrich another country.

Iraq War

Mr Trump said he opposed the war in Iraq before it began.

But during the buildup to the war, he expressed his support in an interview with Howard Stern, according to audio unearthed by BuzzFeed.

Troop Withdrawal

Mr Trump accused Mrs Clinton and President Barack Obama of withdrawing troops and leaving a vacuum in Iraq and Syria, which allowed the Islamic State to take root.

In fact, Mrs Clinton advocated arming moderate rebels in Syria and said afterward that Mr Obama's refusal to do so may have left a vacuum there. She also privately backed a Pentagon proposal to leave a larger residual force in Iraq than the administration ended up leaving.

Nato

Mr Trump was correct in asserting that many Nato countries do not contribute their full share to Nato - a complaint Mr Obama and a former defence secretary, Mr Robert Gates, have also voiced.

But he was wrong about Nato failing to fight terrorism. Nato was in Afghanistan starting in 2003 - part of the battle against Al-Qaeda.

Economy - Trans-Pacific Partnership

Mrs Clinton said, in defence of her flip-flop on the Trans-Pacific Partnership trade deal, that she had "hoped it would be a good deal" but when it was negotiated, she did not agree with the terms.

In fact, Mrs Clinton spoke out more than 40 times in favour of the trade deal, saying it would be a "strategic initiative that would strengthen the position of the United States in Asia", without making her support contingent on how it would turn out.

China's currency

Mr Trump said China is "devaluing their currency" to gain an economic advantage.

This is an outdated accusation.

Countries that hold down the value of their currency can sell goods in other countries more cheaply. And many economists see evidence that China suppressed the value of its currency for years, contributing to its rise as an industrial power. But in recent years, China has sought to stabilise and even increase the value of its currency, part of a broader shift in its economic policies. There is no evidence that China is currently engaging in currency devaluation.

Energy and the environment

Mrs Clinton accused Mr Trump of saying that climate change was a hoax perpetrated by the Chinese. Mr Trump responded: "I do not say that."

But in 2012, Mr Trump tweeted: "The concept of global warming was created by and for the Chinese in order to make US manufacturing non-competitive."

Over the past year, Mr Trump has repeatedly called climate change a hoax, and said he is "not a believer" in the established science of human-caused climate change.

Trump's new hotel

Mr Trump said his Trump International Hotel is next door to the White House.

It is certainly nearby, but it is not quite next door - unless you're flying in a Trump helicopter. Walking from the White House to the hotel takes about 15 minutes, according to Google Maps. If you grab a taxi or Uber, you can cut that down to about six minutes, though it will probably take a bit longer if you drive yourself - finding a place to park in downtown Washington can be a chore.

Family loan

Mrs Clinton said it was US$14 million in loans from Mr Trump's father that helped him get his real estate business off the ground.

Mr Trump said it was just a "small" loan. A recent Wall Street Journal article notes a series of loans and gifts Mr Trump received from his father, citing a casino disclosure document from 1985 showing that Mr Trump owed his father and his father's company about US$14 million.